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a(n) = 2*(n!)^2.
5

%I #38 Sep 08 2022 08:44:57

%S 2,2,8,72,1152,28800,1036800,50803200,3251404800,263363788800,

%T 26336378880000,3186701844480000,458885065605120000,

%U 77551576087265280000,15200108913103994880000,3420024505448398848000000,875526273394790105088000000,253027093011094340370432000000

%N a(n) = 2*(n!)^2.

%C a(n) = automorphism group order for the complete bipartite graph K_{n,n}. - Avi Peretz (njk(AT)netvision.net.il), Feb 21 2001

%C For n > 1, also the order of automorphism group for the n X n rook graph. - _Eric W. Weisstein_, Jun 20 2017

%C Also the number of (directed) Hamiltonian paths in K_{n,n}. - _Eric W. Weisstein_, Jul 15 2011

%C For n>=1, a(n) is the number of ways to arrange n men and n women in a line so that no two people of the same gender are adjacent. - _Geoffrey Critzer_, Aug 24 2013

%C Also the number of (directed) Hamiltonian paths in the (n+1)-barbell graph. - _Eric W. Weisstein_, Dec 16 2013

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GraphAutomorphism.html">Graph Automorphism</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BarbellGraph.html">Barbell Graph</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CompleteBipartiteGraph.html">Complete Bipartite Graph</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HamiltonianPath.html">Hamiltonian Path</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RookGraph.html">Rook Graph</a>

%F a(n) = 2*A001044(n)

%p seq(mul(n!*k!, k=1..2), n=0..17); # _Zerinvary Lajos_, Jul 01 2007

%t 2(Range[0,20]!)^2 (* _Harvey P. Dale_, Jun 21 2011 *)

%t Table[2 (n!)^2, {n, 0, 20}] (* _Vincenzo Librandi_, Feb 22 2016 *)

%o (Magma) [2*Factorial(n)^2: n in [0..30]]; // _Vincenzo Librandi_, Feb 22 2016

%Y Equals 2 * A001044.

%K nonn

%O 0,1

%A _N. J. A. Sloane_